Four charges of equal magnitude are placed at the corners of a square that measures L on each side. There are two positive charges Q diagonally across from one another, and two negative charges -Q at the other two corners.
How much potential energy is associated with this configuration of charges?
One way to determine the total potential energy is to add up the energy from each interacting pair of charges. There are six pairs to consider. Four pairs have a potential energy given by, for example:
U12 = -KQ2/L
The energy for the two diagonal pairs is of the form:
U13 = +KQ2/(21/2 L)
A second way to answer the question is to re-phrase it as "How much work was required to assemble this set of charges in this configuration?"
Bring the charges in from infinity one at a time.